Abstract
A modification of Kraichnan’s direct interaction approximation ~DIA! @R. H. Kraichnan, J. Math. Phys. 2, 124 ~1961!# for random linear partial differential equations is proposed. The approximation is tested on the specific example of the turbulent advection of a scalar quantity by a random velocity field. It is shown to account for the sweeping more correctly than the DIA. As a result, it is valid for all times and it is able to describe nonstandard diffusive processes ~i.e., superdiffusive and non-Gaussian! for which the DIA is not valid. @S1063-651X~98!50111-0#
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